Algebra 1 Common Core Student Edition, Grade 8-9

Real-world data seldom fall exactly into linear, exponential, or quadratic patterns.

However, you can determine which type of function represents the best possible model

for the data.

Pr o b l em 3 Modeling Real-World Data

Transportation The data at the right give the value of a used car over

time. Which type of function best models the data? Write an equation

to model the data.

-Know w JSf iSif c. pJ g n

The va lu e o f a used Graph the data and then use

car over tim e

Step 1

Graph the data.

The m o s t a p p ro p ria te

model for the data

12,000

9000

<u 3 6000

£

3000

0

2 4 6

Years, x

differences or ratios to find a

model for the situation.

Step 2

Test for a common ratio.

Value of Used Car

0 12,575

1 11,065

(^29750)
38520
4 7540

• 1
  C
  +1 C


• (^1) C


• (^1) c
  0 12,575
  1 11,065
  2 9750
  38520
  47540
  11.065
  12,575
  9750
  11.065
  8520
  9750
  7540
  8520
  0.88
  0.88
  0.87
  0.88
  The graph curves and does not look
  quadratic. It may be exponential.
  Step 3
  Write an exponential model.
  Relate
  Define
  Write
  y = a • V0
  Let a = the initial value, 12,575.
  Let b = the decay factor, 0.88.
  y = 12,575 • 0.88x
  Go t I t? 3. The table shows the annual
  income of a small theater
  company. Which type of
  function best models the
  data? Write an equation
  to model the data.
  The value of the car is roughly 0.88
  times its value the previous year.
  Step 4
  Test two points other than (0,12,575).
  Test (2, 9750): Test (4, 7540)
  y = 12,575 • 0.88z a2
  y « 9738
  y = 12,575 • 0.88*
  y « 7541
  The point (2,9738) is close to the data point
  (2, 9750). The point (4, 7541) is close to the data
  point (4, 7540). The equation y = 12,575 • 0.88x
  models the data.
  Theater Company Annual Income
  Year 0123 4
  In c o m e ($) 18,254 18,730 19,215 19,695 20,175
  Po w erAlg eb ra.com Lesso n 9-7 Li n ear , Q u ad r at i c, an d Exp o n en t i al M o d els 591